Will pee damage maple hardwoods that have NOT yet been finished?
If you have dark stains in the wood, and an odor that goes with it, you can certainly try bleaching with the strongest wood bleach available. Do this after all the floor sanding is done, but before any finish goes on. Try a wood bleach called Klean Strip at http://www.kleansrtip.com. It will turn the dark areas an off white color.
The off white colored spots will need a light colored wood stain to blend them in to the rest of the floor. It’s quite an art. You will want the color to blend in with the final finished color of the floor, not the bare wood. Test for the finished color of the wood by splashing some naphtha on the clean wood. You will have to fine sand the spot before staining, but be careful not so sand out the bleached effect. Then complete the finishing of your floors.
And lastly, try major repairs, or replacements. Or a combination of all of these methods. Find an old (or young) floor master in your area, that does these things, and will give you advise in person. But you certainly can do the bleaching yourself.
Oh, and if you just have an odor and no urine stain, try the Cleaning Center at http://www.cleanreport.com for their DXO odor remover.